We make the case that psychologists should make wider use of structural econometric methods. These methods involve the development of maximum likelihood estimates of models, where the likelihood function is tailored to the structural model. In recent years these models have been developed for a wide range of behavioral models of choice under uncertainty. We explain the components of this methodology, and illustrate with applications to major models from psychology. The goal is to build, and traverse, a constructive bridge between the modeling insights of psychology and the statistical tools of economists.

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We make the case that psychologists should make wider use of econometric
methods for the estimation of structural models. These methods involve the
development of maximum likelihood estimates of models, where the likelihood
function is tailored to the structural model. In recent years these models have been
developed for a wide range of behavioral models of choice under uncertainty. We
explain the components of this methodology, and illustrate with applications to
major models from psychology. The goal is to build, and traverse, a constructive
bridge between the modeling insights of psychology and the statistical tools of
economists.

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The most popular models of decision making use a single criteria to evaluate
projects or lotteries. However, decision makers may actually consider multiple
criteria when evaluating projects. We consider a dual criteria model from psychology.
This model integrates the familiar tradeoffs between risk and utility that economists
traditionally assume, allowance for rank-dependent decision weights, and
consideration of income thresholds. We examine the issues involved in full
maximum likelihood estimation of the model using observed choice data. We
propose a general method for integrating the multiple criteria, using the logic of
mixture models, which we believe is attractive from a decision-theoretic and
statistical perspective. The model is applied to observed choices from a major natural
experiment involving intrinsically dynamic choices over highly skewed outcomes.
The evidence points to the clear role that income thresholds play in such decision
making, but does not rule out a role for tradeoffs between risk and utility or
probability weighting.

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Subjective beliefs play a role in many economic decisions. There is a large theoretical
literature on the elicitation of beliefs, and an equally large empirical literature. However, there is a
gulf between the two. The theoretical literature proposes a range of procedures that can be used to
recover beliefs, but stresses the need to make strong auxiliary assumptions or “calibrating
adjustments” to elicited reports in order to recover the latent belief. With some notable exceptions,
the empirical literature seems intent on either making those strong assumptions or ignoring the need
for calibration. We make three contributions to bridge this gulf. First, we offer a general theoretical
framework in which the belief elicitation task can be viewed as an exchange of state-dependent
commodities between two traders. Second, we provide a specific elicitation procedure which has clear
counterparts in field betting environments, and that is directly motivated by our theoretical
framework. Finally, we illustrate how one can jointly estimate risk attitudes and subjective beliefs using
structural maximum likelihood methods. This allows the observer to make inferences about the
latent subjective belief, calibrating for virtually any well-specified model of choice under uncertainty.
We demonstrate our procedures with an experiment in which we elicit subjective probabilities over
three future events and one fact.

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It is intuitive that decision-makers might have attitudes towards uncertainty just as they
might have attitudes towards risk. However, it is only recently that this intuitive notion has been
formalized and axiomatically characterized. We estimate the extent of uncertainty aversion in a
manner that is parsimonious and consistent with theory. We demonstrate that one can jointly
estimate attitudes towards uncertainty, attitudes towards risk, and subjective probabilities in a
rigorous manner. Our structural econometric model constructively demonstrates the theoretical
claims that it is possible to define uncertainty aversion in an empirically tractable manner. Our
results show that attitudes towards risk and uncertainty can be different, qualitatively and
quantitatively, and that allowing for these differences can have significant effects on inferences about
subjective probabilities.

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Subjective probabilities play a central role in many economic decisions, and act as an
immediate confound of inferences about behavior, unless controlled for. Several procedures to
recover subjective probabilities have been proposed, but in order to recover the correct latent
probability one must either construct elicitation mechanisms that control for risk aversion, or
construct elicitation mechanisms which undertake “calibrating adjustments” to elicited reports. We
illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration
adjustments that theory calls for. We illustrate this approach using data from a controlled experiment
with real monetary consequences to the subjects. This allows the observer to make inferences about
the latent subjective probability, under virtually any well-specified model of choice under subjective
risk, while still employing relatively simple elicitation mechanisms.

Subjective probabilities play a role in many economic decisions. There is a large
theoretical literature on the elicitation of subjective probabilities, and an equally large empirical
literature. However, there is a gulf between the two. The theoretical literature proposes a range of
procedures that can be used to recover subjective probabilities, but stresses the need to make strong
auxiliary assumptions or “calibrating adjustments” to elicited reports in order to recover the latent
probability. With some notable exceptions, the empirical literature seems intent on either making
those strong assumptions or ignoring the need for calibration. We illustrate how one can jointly
estimate risk attitudes and subjective probabilities using structural maximum likelihood methods. This
allows the observer to make inferences about the latent subjective probability, calibrating for
virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with
experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective
beliefs assuming that choices are made consistently with expected utility theory or rank-dependent
utility theory. Inferred subjective probabilities are significantly different when calibrated according to
either theory.

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We develop an extension of the familiar linear mixed logit model to allow
for the direct estimation of parametric non-linear functions defined over structural
parameters. A classic application is the estimation of coefficients of utility functions
to characterize risk attitudes. There are several unexpected benefits of this extension,
apart from the ability to directly estimate structural parameters of theoretical interest.

Experimental data exhibit considerable individual heterogeneity. We review
the econometric methods employed to characterize that heterogeneity. We pay
particular attention to the trade-off between collecting and allowing for observable
characteristics, such as the familiar demographics, and the use of statistical methods
to allow for unobserved individual heterogeneity. We demonstrate that these tools
are complementary.